Finite Group Databasebeta

← #22615083

Subgroups — #22615083

Order 9344.

672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556571C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D73C211yesmaximal, characteristic
3#17988513C211yesmaximal, characteristic, complemented
4#17988500C211yesmaximal, characteristic, complemented
5#17988499C211yesmaximal, characteristic, complemented
6#17988480C212yesmaximal, complemented
7#17988479C212yesmaximal, complemented
8#17988449C212yesmaximal, complemented
9#17988442C212yesmaximal
10#17988434C211yesmaximal, characteristic, complemented
11#397×C73C211yesmaximal, characteristic, complemented
12C24×D73C2211yescharacteristic
13C22×Dic146C2211yescharacteristic, complemented
14C22×C4×D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556571—24no—
17C2×C4⋊Dic73C2212yescomplemented
18C2×C22⋊Dic73C2211yescharacteristic
19C2×C22⋊Dic73C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C22⋊C4×D73—24no—
27C2×C4×Dic73C2212yescomplemented
28#14556498C2211yescharacteristic, complemented
29#14556498C2212yescomplemented
30#14556498C2212yescomplemented
31#14556498C2212yescomplemented
32C2×C4⋊C4×C73C2211yescharacteristic, complemented
33C2×C22⋊C4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35#95×C73C2211yescharacteristic, complemented
36#95×C73C2212yescomplemented
37C23×D73—22no—
38C23×D73—22no—
39C23×D73—22no—
40C23×D73—24no—
41C23×D73—42no—
42C23×D73C2311yescharacteristic
43C23×D73C2311yescharacteristic
44C2×Dic146—22no—
45C2×Dic146—42no—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2312yes—
48C22×Dic73C2312yes—
49C22×Dic73C2311yescharacteristic
50C2×C4×D73—22no—
51C2×C4×D73—24no—
52C2×C4×D73—42no—
53C2×C4×D73D414yes—
54C4⋊Dic73—24no—
55C22⋊Dic73—22no—
56C22⋊Dic73—42no—
57#11924005—24no—
58#11924005—24no—
59#11924005—24no—
60#11924005—22no—
61#11924005—22no—
62#11924005—42no—
63C4×Dic73—42no—
64C24×C73C2311yescharacteristic
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2312yes—
67C22×C4×C73C2312yes—
68C22×C4×C73C2311yescharacteristic
69C4⋊C4×C73—22no—
70C22⋊C4×C73—24no—
71C22⋊C4×C73—22no—
72C23×C73—21no—
73C23×C73—21no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73#4112yes—
77C23×C73C2411yescharacteristic
78C22×D73—21no—
79C22×D73—21no—
80C22×D73—22no—
81C22×D73—28no—
82C22×D73—21no—
83C22×D73—22no—
84C22×D73—21no—
85C22×D73—22no—
86C22×D73—48no—
87C22×D73—48no—
88C22×D73—44no—
89C22×D73—44no—
90C22×D73C2×D412yes—
91C22×D73#4112yes—
92C22×D73#4114yes—
93C2×C4×C73—22no—
94C2×C4×C73—21no—
95C2×C4×C73—22no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73C2×D412yes—
103C2×Dic73—22no—
104C2×Dic73—21no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73C2×D412yes—
113C4×D73—44no—
114C4×D73—44no—
115Dic146—44no—
116C22×C73—22no—
117C22×C73—24no—
118C22×C73—41no—
119C22×C73—41no—
120C22×C73—42no—
121C22×C73C22×D411yescharacteristic
122C22×C73C2×#4111yescharacteristic
123C22×C73C2×#4112yes—
124C22×C73C2×#4111yescharacteristic
125C22×C73H(5,𝔽2)12yes—
126C2×D73—22no—
127C2×D73—22no—
128C2×D73—24no—
129C2×D73—24no—
130C2×D73—22no—
131C2×D73—24no—
132C2×D73—416no—
133C2×D73—41no—
134C2×D73—41no—
135C2×D73—42no—
136C2×D73#12414yes—
137C4×C73—22no—
138C4×C73—42no—
139C4×C73—41no—
140C4×C73—42no—
141Dic73—22no—
142Dic73—41no—
143Dic73—42no—
144Dic73—42no—
145C2×C73—42no—
146C2×C73#52511yescharacteristic
147C2×C73C2×#12411yescharacteristic
148C2×C73#53411yescharacteristic
149C2×C73#55112yes—
150C2×C73#55112yes—
151D73—24no—
152D73—42no—
153#2561—731nomaximal, Sylow
154C73#256111yescharacteristic, complemented, Sylow
155C2×C22⋊Q8—731no—
156C22×C22⋊C4—731no—
157#397—731no—
158#397D7311yescharacteristic, complemented
159#393—731no—
160#393—731no—
161#388—732no—
162#388—732no—
163#381—732no—
164#379—732no—
165C4×C22⋊C4—731no—
166C25—731no—
167C22×Q8—731no—
168C23×C4—731no—
169C23×C4—731no—
170C22⋊Q8—1464no—
171C2×C4⋊C4—732no—
172C2×C4⋊C4C2×D7311yescharacteristic, complemented
173C2×C22⋊C4—732no—
174C2×C22⋊C4—732no—
175C2×C22⋊C4—731no—
176C2×C22⋊C4—731no—
177C2×C22⋊C4—731no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4—732no—
181C2×C22⋊C4—1464no—
182C2×C22⋊C4C2×D7311yescharacteristic
183C2×C22⋊C4C2×D7312yes—
184C2×C42—732no—
185#95—731no—
186#95—732no—
187#95—732no—
188#95—732no—
189#95C2×D7311yescharacteristic, complemented
190#95C2×D7312yescomplemented
191C24—2922no—
192C24—731no—
193C24—731no—
194C24—1464no—
195C24—1462no—
196C24—1462no—
197C24—1462no—
198C24C22×D7311yescharacteristic
199C2×Q8—2922no—
200C2×Q8—1462no—
201C22×C4—2922no—
202C22×C4—734no—
203C22×C4—731no—
204C22×C4—731no—
205C22×C4—732no—
206C22×C4—732no—
207C22×C4—1462no—
208C22×C4—1464no—
209C22×C4C22×D7311yescharacteristic
210C22×C4C22×D7312yes—
211C22×C4C22×D7312yes—
212C22×C4C22×D7311yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—1464no—
215C22⋊C4—24no—
216C22⋊C4—22no—
217C22⋊C4—2922no—
218C22⋊C4—2922no—
219C22⋊C4—1462no—
220C22⋊C4—1464no—
221C22⋊C4—1464no—
222C22⋊C4—1464no—
223C22⋊C4—1462no—
224C22⋊C4—1462no—
225C42—2922no—
226C23—21no—
227C23—22no—
228C23—21no—
229C23—22no—
230C23—2928no—
231C23—2924no—
232C23—2924no—
233C23—2928no—
234C23—732no—
235C23—734no—
236C23—732no—
237C23—1468no—
238C23—1461no—
239C23—1462no—
240C23—1461no—
241C23—1462no—
242C23—1461no—
243C23—1461no—
244C23—1462no—
245C23#1192402712yes—
246C23C23×D7311yescharacteristic
247Q8—2924no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—2924no—
258C2×C4—2924no—
259C2×C4—732no—
260C2×C4—1461no—
261C2×C4—1462no—
262C2×C4—1462no—
263C2×C4—1462no—
264C2×C4—1462no—
265C2×C4—1462no—
266C2×C4—1462no—
267C2×C4—1462no—
268C2×C4—1462no—
269C2×C4D4×D7312yes—
270C22—24no—
271C22—22no—
272C22—41no—
273C22—42no—
274C22—41no—
275C22—29216no—
276C22—2921no—
277C22—2922no—
278C22—2921no—
279C22—734no—
280C22—1464no—
281C22—1462no—
282C22—1462no—
283C22—1464no—
284C22—1464no—
285C22—1462no—
286C22C2×D4×D7311yescharacteristic
287C22#41×D7312yes—
288C22#41×D7311yescharacteristic
289C22C2×#1192402711yescharacteristic
290C22#1455663712yes—
291C4—22no—
292C4—42no—
293C4—42no—
294C4—41no—
295C4—2922no—
296C4—2922no—
297C4—2921no—
298C4—1462no—
299C2—42no—
300C2—2922no—
301C2—1464no—
302C2#1798909711yescharacteristic
303C2#124×D7311yescharacteristic
304C2#1798914811yescharacteristic
305C2#1798926012yes—
306C2#1798926212yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2561
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14556571C2semidirect
3. #17988513C2semidirect
4. #17988500C2semidirect
5. #17988499C2semidirect
6. #17988480C2semidirect
7. #17988479C2semidirect
8. #17988449C2semidirect
10. #17988434C2semidirect
11. #397×C73C2semidirect
13. C22×Dic146C22semidirect
17. C2×C4⋊Dic73C22semidirect
27. C2×C4×Dic73C22semidirect
28. #14556498C22semidirect
29. #14556498C22semidirect
30. #14556498C22semidirect
31. #14556498C22semidirect
32. C2×C4⋊C4×C73C22semidirect
35. #95×C73C22semidirect
36. #95×C73C22semidirect
154. C73#2561semidirect
158. #397D73semidirect
172. C2×C4⋊C4C2×D73semidirect
189. #95C2×D73semidirect
190. #95C2×D73semidirect